It depends on what type of asnwer will satisfy you. If you want a scientifically rigorous answer, I don't think that will be forthcoming (not sure if double blind testing has been done for the LS3/5 speakers).
But if you want to know why owners of those speakers like them so much, I can give my anecdotal report, as I own the Spendor version of the 3/5s.
For my 2 channel music listening, I've owned many speakers (and still own 6 different "high end" speakers), and every time I put the little Spendors in my system I'm utterly beguiled. They have a wonderful combination of tonal warmth with clarity, and they sound smooth, just enough to take the edge off many recordings. (Smooth but not "dark" and rolled off - they sound both smooth but super "open" and sparkly). They soundstage like demons, and voices sound more "natural" and human to my ear than through most speakers. Tonally they seem to reproduce acoustic sounds convincingly to my ears. So when I listen to an acoustic guitar track, or a recording of my own acoustic guitar through the 3/5s, it sounds "right." There's that balance of warmth like there's a guitar body, and the "golden sparkle" of the upper strings, much like I hear in real guitars. I can play my guitar right after listening to my recording of that guitar through the spendors and there isn't a big disconnect, it's "yeah, that's basically right."
And when a speaker can do that, for me it's one of my greatest joys in audio.
Even more subjectively, and hard to describe, there is something so "balanced" in their presentation that it's like the "mix" of music tracks seem to "make sense," feel balanced. Even when I put them in place of large floor standing speakers the little 3/5s are hard to pull back out of my 2 channel system.
People around here don't tend to go in for such subjective descriptions, but...since you asked why some people like those speakers and I own a pair...well...there's why